{
  "annotation_id": "c50dae5e-5f00-486d-872c-c7b757d834a8",
  "date_created": "2026-02-17T05:53:24.341000Z",
  "date_modified": "2026-02-17T05:53:24.341000Z",
  "file_hash": "f1d3775a7fca36dcfdb15f09fd163806b2740bdcc01067f3e06e50c8c4762de6",
  "private": false,
  "record": {
    "abstract": "We determine an infinite family of linear identities for the number $A_4(n)$ of partition pairs of $n$ with $4$-cores by employing elementary $q$-series techniques and certain $3$-dissection formulas. We then discover an infinite family of congruences for $A_4(n)$ as a consequence of these linear identities.",
    "arxiv_id": "2601.10438",
    "authors": [
      "Russelle Guadalupe"
    ],
    "categories": [
      "math.NT",
      "math.CO"
    ],
    "license": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
    "title": "Linear identities for partition pairs with $4$-cores",
    "url": "https://arxiv.org/abs/2601.10438",
    "version": "v1"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "e20328d1-3be4-4058-bde7-988c6a030e59",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}